The Finite Improbability Calculator

by Wesley R. Elsberry

The Finite Improbability Calculator is a collection of routines
to permit exploration of very small probabilities. Many
antievolutionary arguments are based upon an argument from
improbability: some phenomenon is so improbable that it must
be due to an intelligent agent.

Usage:

Select an operation to perform from the list.

Enter the parameters for the operation.

Press the button for the operation.

Results appear in a separate browser window. (You may need to turn off anti-popup services for this page.)

Notes on calculations

Factorial: The point here is to permit calculation of
factorial(n) where n can be a large number, say the number of proteins
which an organism codes for. However, even a "double"
floating-point number overflows at 1.7e308. So factorials are
calculated here using a logarithmic representation. The Stirling
approximation is used for very large n, and a logarithmic version of
the classical iterative method is used for smaller n. Stirling's
approximation is taken as

Specified Anti-Information is an application of the "universal
distribution" of Kirchherr et alia 1997, expounded in Elsberry and
Shallit 2003. SAI is a framework intended as an alternative to
Dembski's "design inference". The SAI of a bit string is defined
as

SAI = max(0,|y| - C(y))

where |y| is the length of the bit string of interest and
C(y) is the Kolmogorov complexity of y. Since C(y) is
uncomputable, mostly we should speak of Known Specified
Anti-Information, which is just the maximum SAI that can
be established by application of known compression
techniques.

SAI is defined for bit strings, but often we deal with
strings based on a symbol set with cardinality > 2. It is
straightforward to determine the length of a bit string
needed to represent such a string, though, using the "change of
base" function presented earlier. The second part of the SAI
section permits SAI to be calculated for such strings.

Something to note here is the apparent difference in
ease of application of SAI with the various measures
introduced by Dembski.

The discussion on page 301 implies that functional proteins may
themselves be considered "discrete combinatorial objects" to
which this formula would apply. With a little exploration, then,
one can verify that any functional protein of length 1153 or greater
has an origination probability smaller than Dembski's "universal
small probability".

plocal calculation (as per NFL p.293):

plocal = (units in system * substitutions / total different
units) (units in system * copies)

There is a discrepancy between the result which Dembski reports
for his
example calculation of an M/N ratio on p.297 and what the Finite
Improbability
Calculator reports. Plug in symbols=30, length=1000,
tolerance=0.1, and
identity=0.2 and the result comes out as 5.555117e-223, whereas
Dembski
reports 10^-288, or a factor of 10^-65 off. Jeff Shallit noted
this
error in Dembski's text some time back.

The Finite Improbability Calculator was first coded in spring of 2002,
following publication of William Dembski's book, "No Free Lunch". The
original utilized a Perl CGI script. The FIC was ported to a PHP
instantiation in January, 2004, with routines added for calculating
Specified Anti-Information.

The name of this page was inspired by "The Hitchhiker's Guide to the
Galaxy" by the late great Douglas Adams.